Pre-processing Nonlinear Output Regulation with Non-Vanishing Measurements

The paper deals with the output regulation problem of linear and nonlinear systems in the presence of measurements that, besides the regulation error, might include also extra outputs non-vanishing in steady state. We first show that, for linear systems, any “pre-processing” internal model-based solution solving the problem in a robust way necessarily relies on a stabilizer blocking the steady state effect of the extra measurements through properly located zeros. Motivated by this, a nonlinear pre-processing design strategy, relying on a “washout filter” processing the non-vanishing measurements and generating a new output having zero steady state, is presented for nonlinear systems in a semiglobal setting. A new nonlinear non-resonance condition, underlying the stabilizability by output feedback of the cascade of the plant and the filter, is introduced.